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# Title: [Johannis Wallis S. T. D. Geometriae Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica] Johannis Wallis S. T. D. Geometriæ Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica (shelfmarks Leibn. Marg. 100:1/2, Stück 1; Leibn. Marg. 100:1/2)
# Folio 624, page id 851387705:0644
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DL1V
A Deoque G, in P consticurum cencrum Siquilibrii, inde vi amoveatur; se
Lrelticue sibi permista Libra, gravicace sua: Si consticurum in S, amorea-
TUT: non eo restituetur, Sed deorlum ad P FerCTUT.
Quod aurem de Libra, Stricte sumpta, ponderibusque libere appentis (adeoque
in plano aHOTILOMLEM PetPHICulari) ostensum elt: Pariter ostendetur, MMa
tis mucandis, in quaris alia ri. Puta; Si planum S F. P non crectum sIC, Sed urcun-
que obliquum, in quo AB libra incelligatur, cum super illud moveri appenla pon-
dera: Similiter enim (ex 20. Cap. 2.) omnia procedeM i SL al HOIILBIICALCM
rectam in eo plano normaliret potitam (quod Perpendiculi (_CCe a ACLL HIHUS)
aique SP verpendiculo ad Cemrum PCErX. AULCtIaI; SI MI LIOTLLBCa atorC
planc modo proccdei demonttracio.
quocunque Plano incelligatur L ibra, (sive quod Libra instar cst) eique in A e
B applicarae vires quaecunque secundum Directionem ipli SP parallelam: Fodem
ex lplislibere dependent sartas ua tant ea puncta a Centro Libra.
a alor ncete ret edere (eodem seilicer quae in eodem Bra
Alcendendo vel Sclcenacuc, cum ipsius puncta singula, tum quae
Si circa Cenerum suum rotetur Libra; in ea ratione moventur, vel
rca L. Cen Locetur Libra AB. Dico iptius puncta LISua, IL A, B, D.
saiste
chio; quae in contrario, contrario momu;) qua distant a C CentrO.
Deleribune enim A, B, D, puncta (propter eundem rel aequales angulos ad C)
limiles arcus (puca A a, BB, Dd,) qui itaque cum ipsi, cum ec iptorum alticndi-
nes perpendicuto menturatae (puta Aa, B B, DS,) Tunc (propcer tisuras similes
ee similiter licas, Talcem limu concrario posiras, quod hic tancundem tacic) radiis
luis, hoc est,s d Ceviro distantiis C A, CB, C. D, proportionales: adeoque et (Per
20. Cap. 2.) Punctorum A, B, D, Ascensus, Delcentutre. Ouod crac demonstran-
dum.
Ouodque de iptis punetis ostenditur; perinde verum est de Ponderibus inde li-
bere dependencibus; vel per Prop. 4. hujus; rel etiam, quia, quemeunque arcum
deleribie, verti gracia, B punctum; huic similem ec aequalem de similicer litum, de
scribet ab eo libere dependens P, (utpore quod cidem, per 30. Cap. 2. perpendi
culariter ubique Tubelt; e propier aequalem fili longicudinem, in eadem distan-
eia.) Adeoque cancundem vel ascendu vel descendit; hoc est ( per modo demon-
Arata) in racione distantiarum punctorum appentionis d Centro. Ouod etiam erat
Demonstrandum.